Metre Bridge

The metre bridge (also called a slide-wire bridge) realises the Wheatstone bridge principle (Section 3.12) using a one-metre length of uniform resistance wire, mounted on a metre scale, in place of two of the bridge's four resistance arms. This makes it possible to vary the ratio of those two arms CONTINUOUSLY, simply by sliding a contact (the jockey) along the wire, rather than needing a second adjustable resistance box.

Construction. A uniform wire, exactly $100\ \text{cm}$ long, is stretched along a metre scale. A known resistance $R$ (from a resistance box) is connected in one gap at one end of the wire, and the unknown resistance $X$ to be determined is connected in the gap at the other end. A battery (with a key and rheostat to limit and adjust the current) is connected across the two outer ends of this series arrangement, so current flows along the whole length: through $R$, along the wire, and through $X$. A galvanometer is connected between the jockey (which can touch the wire at any point) and the junction between the two resistance gaps.

Balance condition. The wire itself, being uniform, has a resistance directly proportional to its length. If the jockey is placed at a distance $l$ (in cm) from the end nearer the KNOWN resistance $R$, the wire is thereby divided into two effective resistances in the ratio $l : (100-l)$ -- these two wire-sections play the role of the "ratio arms" $P$ and $Q$ of the general Wheatstone bridge, with $R$ and $X$ playing the role of the other two arms. At the balance point (found by sliding the jockey until the galvanometer shows zero deflection), the general balance condition $P/Q=R/S$ of Section 3.12 becomes

(with the convention that $l$ is measured from the end nearer $R$; if instead measured from the end nearer $X$, the formula becomes $X = R\,l/(100-l)$ -- the two conventions simply exchange $l$ and $100-l$, so it is essential to state clearly, when reporting a reading, from WHICH end $l$ was measured). …